Robert L Bryant, J. M. Kreps Professor

Office Location:	119 Mathematical Sciences Research Institute
Office Phone:	(510) 642-0143
Email Address:

Typical Courses Taught:

• MATH 103X, HONORS INTERMED CALCULUS

• MATH 123S, GEOMETRY Synopsis

• MATH 245, COMPLEX ANALYSIS Synopsis

• MATH 250, COMPUTA ALGEBRA/GEOMETRY

• MATH 267, DIFFERENTIAL GEOMETRY

• MATH 268, Topics in DIFFERENTIAL GEOMETRY: Symplectic Geometry Synopsis

  The first third of the course is devoted to 'classical' symplectic geometry: Lagrangians, Legendre transformations, Hamiltonians, symplectic manifolds and the Darboux-Weinstein theorem, symmetries and conservation laws and the Arnold- Liouville theorem, momentum mappings, reduction, and convexity. The second third of the course is devoted to developing elliptic methods: pseudo-holomorphic curves, Gromov compactness and moduli, applications to packing and (non)-squeezing theorems, etc. The final third covers related topics and recent developments, such as relations with toric varieties, representation theory, or other topics that depend on the interests of the class.

• MATH 272, RIEMANN SURFACES Synopsis

Office Hours:

None this academic year

Education:

PhD	University of North Carolina at Chapel Hill	1979
BS	North Carolina State University at Raleigh	1974

Specialties:

Geometry
Mathematical Physics

Research Interests: Nonlinear Partial Differential Equations and Differential Geometry

I'm interested in the geometry of partial differential equations (as always), but, more specifically, I have been thinking about conservation laws for PDE, Finsler geometry, calibrations, holonomy, and trying to learn more about Seiberg-Witten invariants and symplectic geometry.

Areas of Interest:

exterior differential systems
differential geometry
algebraic geometry
Finsler geometry

Keywords:

calibrations • solitons • CR hypersurfaces • exterior differential systems • Finsler

Current Ph.D. Students  

• Conrad A. Hengesbach  
• Abraham D. Smith  
• Feng Xu  

Recently Featured in:

• Bryant named MSRI's Director, May 01, 2007

Recent Publications   (search)

1. with G. Manno, V. Matveev, A solution of a problem of Sophus Lie: Normal forms of 2-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437--463 [3592]  [abs]
2. with M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures (Preprint, 2008) [arXiv:0801.0300v1 [math.DG]]  [abs]
3. Nonembedding and nonextension results in special holonomy, in Proceedings of the August 2006 Madrid conference in honor of Nigel Hitchin's 60th Birthday, edited by Jean-Pierre Bourguignon, Simon Salamon, and Oscar Garcia Prada (Submitted, Fall, 2007), Oxford University Press
4. Geodesically reversible Finsler 2-spheres of constant curvature, in Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by P. A. Griffiths, vol. 11 (Winter, 2006), World Scientific [math.DG/0407514]  [abs]
5. On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561--606 [math.DG/0508428]  [abs]

Selected Invited Lectures

1. The classification of reversible Finsler metrics on the 2-sphere with constant flag curvature, November 18, 2005, "On Finsler geometry" workshop. CIRM Luminy, France [html]    
2. The geometry of almost complex 6-manifolds, October 29, 2005, Nara University, Nara Japan [pdf]    
3. Existence and uniqueness for gradient Kahler-Ricci solitons, May 19, 2005, Ecole Polytechnique, Palaiseau, France [html]    
4. MAA Short Course on Geometry and the Calculus of Variations, March 11, 2005, MAA Southeastern 84th Meeting at Meredith College [htm]    
5. Calibrations in Geometry and Topology, October 22, 2004, Institute for Advanced Study, Princeton, NJ    

Recent Grant Support

• The Geometry of Partial Differential Equations, NSF, Proposal No. 0604195, 2006/07-2007/06.      
• Microstates to Macrodynamics: A New Mathematics of Biology, Princeton University, Princeton Univ. Sub. #1-P3836564, 2005/09-2006/09.      

Conferences Organized

• Annual East Coast Geometry Festival, Member of Organizing Board, 1 January 1990  
• Workshop on Calibrations, Conference Organizer, June 26, 2006 - June 30, 2006  
• Singularities in Analysis, Geometry, and Topology: A Conference Honoring the Retirements of F. Reese Harvey and John Polking, Scientific Advisor on Organizing Committee, November 11, 2005 - November 13, 2005  
• International Symposium on Finsler Geometry, Member of organizing committee, August 10, 2004 - August 14, 2004  
• Oberwolfach Bi-Annual Differential Geometry in the Large, co-Organizer, June 15, 2001 - May 31, 2004  
• MSRI Year-Long Program in Geometry (2003-2004), co-Organizer, 2001-04